how to get τ = Y ( q , q ˙ , q ¨ ) χ the inertia matrix X？

[cherishyuan]

In example ：

#Exemple: compute the full regressor matrix 
W = reg.computeFullRegressor(q, qp, qpp)
#Exemple : compute the reduced rgressor matrix
W_ = reg.computeReducedRegressor(q, qp, qpp,1e-6)

How do I get the corresponding inertia matrix X？I don't find the corresponding documentation

THanks!

[wissem01chiha]

Hi @cherishyuan,

Thanks very much for your interest in my work. The $X$ variable is not only the inertial matrix, but rather a $1 \times k$ vector which contains the inertial values of the robot in the first $6 \times n$ elements. Here, $n$ is the number of robot links (since each link’s inertia tensor can be represented by 6 elements: $I_{xx}$, $I_{yy}$, $I_{zz}$, $I_{xz}$, $I_{xy}$, $I_{yz}$). The remaining elements represent other variables related to friction or stiffness parameters of each joint. The general form of $X$ is:

$$ \mathbf{X} = [I_{xx,1}, I_{yy,1}, I_{zz,1}, I_{xz,1}, I_{xy,1}, I_{yz,1}, \dots, I_{xx,n}, I_{yy,n}, I_{zz,n}, I_{xz,n}, I_{xy,n}, I_{yz,n}, f_{c,1}, f_{c,1}, \dots, k_1, k_2, \dots, k_n, \dots] $$

This vector is the scope of the project, which is to extract it from real-world experiments. There are two ways to obtain the inertial parameters:

1. Referring to the datasheet of your robot and extracting the values directly (note that these values may not be very accurate for your experiments, so use them as an initial guess to start the identification routines and optimization of $X_0$). For example, for Kinova Gen3, you can find them here on page 205.

2. Setting random initial values and running one of the optimization scripts to find the suitable ones. This will generate the vector $X$ as a .npy file, which can be loaded directly into Python. (I have removed the specific values for the Kinova Gen3.)

For more information about the results (figures, error values, etc.) and experimentation, you can find it here.

[cherishyuan]

@wissem01chiha commented on Dec 25, 2024, 5:50 PM GMT+8:

Hi @cherishyuan,

Thanks very much for your interest in my work. The X variable is not only the inertial matrix, but rather a 1 × k vector which contains the inertial values of the robot in the first 6 × n elements. Here, n is the number of robot links (since each link’s inertia tensor can be represented by 6 elements: I x x , I y y , I z z , I x z , I x y , I y z ). The remaining elements represent other variables related to friction or stiffness parameters of each joint. The general form of X is:

X = [ I x x , 1 , I y y , 1 , I z z , 1 , I x z , 1 , I x y , 1 , I y z , 1 , … , I x x , n , I y y , n , I z z , n , I x z , n , I x y , n , I y z , n , f c , 1 , f c , 1 , … , k 1 , k 2 , … , k n , … ]

This vector is the scope of the project, which is to extract it from real-world experiments. There are two ways to obtain the inertial parameters:

1. Referring to the datasheet of your robot and extracting the values directly (note that these values may not be very accurate for your experiments, so use them as an initial guess to start the identification routines and optimization of X 0 ). For example, for Kinova Gen3, you can find them here on page 205.

2. Setting random initial values and running one of the optimization scripts to find the suitable ones. This will generate the vector X as a .npy file, which can be loaded directly into Python. (I have removed the specific values for the Kinova Gen3.)

For more information about the results (figures, error values, etc.) and experimentation, you can find it here.

Thank you for your reply. I know how to solve the dynamic parameters, but there seems to be a lack of usable demos. I hope to add usable demos for testing. Thank you for your contribution.

[wissem01chiha]

Hi @cherishyuan, yes, you're right the current documentation lacks a lot of clarification on how to use the tools. I'm working on updating it whenever I have some free time. thank you so much for your feedback, I really appreciate it.